PrescribeInitialEquilibrium

Sets initial zero angular velocity and zero angular acceleration for a rotational connector.

This component establishes an initial equilibrium state for an associated Spline connector by setting its initial angular velocity (w) and initial angular acceleration (a) to zero. It also ensures that the torque (spline.tau) on the connector is zero. The component defines the kinematic relationships where angular velocity (w) is the time derivative of the spline's angle (spline.phi), and angular acceleration (a) is the time derivative of angular velocity, as expressed in the relations section:

$$\begin{array}{rl}w& =\frac{d\text{spline.phi}}{dt}\\ a& =\frac{dw}{dt}\end{array}$$

These initial conditions and definitions ensure the connected rotational system starts from a standstill without any initial torque being applied through this prescription.

Usage

PrescribeInitialEquilibrium()

Connectors

• spline - This connector represents a rotational spline with angle and torque as the potential and flow variables, respectively. (Spline)

Variables

Name	Description	Units
w	Represents the angular velocity of the connector.	rad/s
a	Represents the angular acceleration of the connector.	rad/s2

Behavior

$$\begin{array}{rl}\mathtt{spline}\mathtt{.}\mathtt{tau}\left(t\right)& =0\\ w\left(t\right)& =\frac{\mathrm{d}\mathtt{spline}\mathtt{.}\mathtt{phi}\left(t\right)}{\mathrm{d}t}\\ a\left(t\right)& =\frac{\mathrm{d}w\left(t\right)}{\mathrm{d}t}\end{array}$$

Source

# Sets initial zero angular velocity and zero angular acceleration for a rotational connector.
#
# This component establishes an initial equilibrium state for an associated `Spline` connector
# by setting its initial angular velocity (`w`) and initial angular acceleration (`a`) to zero.
# It also ensures that the torque (`spline.tau`) on the connector is zero.
# The component defines the kinematic relationships where angular velocity (`w`) is the
# time derivative of the spline's angle (`spline.phi`), and angular acceleration (`a`) is the
# time derivative of angular velocity, as expressed in the `relations` section:
# ```math
# \begin{align*}
# w &= \frac{d \text{spline.phi}}{dt}\\
# a &= \frac{dw}{dt}
# \end{align*}
# ```
# These initial conditions and definitions ensure the connected rotational system
# starts from a standstill without any initial torque being applied through this prescription.
component PrescribeInitialEquilibrium
  spline = Spline() [{"Dyad": {"placement": {"icon": {"x1": -50, "y1": 450, "x2": 50, "y2": 550}}}}]
  # Represents the angular velocity of the connector.
  variable w::AngularVelocity
  # Represents the angular acceleration of the connector.
  variable a::AngularAcceleration
relations
  initial w = 0
  initial a = 0
  spline.tau = 0
  w = der(spline.phi)
  a = der(w)
metadata {
  "Dyad": {
    "labels": [
      {"label": "initial w = 0", "x": 500, "y": 150, "rot": 0},
      {"label": "initial a = 0", "x": 500, "y": 800, "rot": 0}
    ],
    "icons": {"default": "dyad://RotationalComponents/Pos-Speed-Acc-Move.svg"}
  }
}
end

Flattened Source

# Sets initial zero angular velocity and zero angular acceleration for a rotational connector.
#
# This component establishes an initial equilibrium state for an associated `Spline` connector
# by setting its initial angular velocity (`w`) and initial angular acceleration (`a`) to zero.
# It also ensures that the torque (`spline.tau`) on the connector is zero.
# The component defines the kinematic relationships where angular velocity (`w`) is the
# time derivative of the spline's angle (`spline.phi`), and angular acceleration (`a`) is the
# time derivative of angular velocity, as expressed in the `relations` section:
# ```math
# \begin{align*}
# w &= \frac{d \text{spline.phi}}{dt}\\
# a &= \frac{dw}{dt}
# \end{align*}
# ```
# These initial conditions and definitions ensure the connected rotational system
# starts from a standstill without any initial torque being applied through this prescription.
component PrescribeInitialEquilibrium
  spline = Spline() [{"Dyad": {"placement": {"icon": {"x1": -50, "y1": 450, "x2": 50, "y2": 550}}}}]
  # Represents the angular velocity of the connector.
  variable w::AngularVelocity
  # Represents the angular acceleration of the connector.
  variable a::AngularAcceleration
relations
  initial w = 0
  initial a = 0
  spline.tau = 0
  w = der(spline.phi)
  a = der(w)
metadata {
  "Dyad": {
    "labels": [
      {"label": "initial w = 0", "x": 500, "y": 150, "rot": 0},
      {"label": "initial a = 0", "x": 500, "y": 800, "rot": 0}
    ],
    "icons": {"default": "dyad://RotationalComponents/Pos-Speed-Acc-Move.svg"}
  }
}
end

Test Cases

No test cases defined.

Related

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